What is the answer to log_{x}(512)= 3/2 ?

The answer to log_{x}(512)= 3/2 is x=64

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log_{x}(512)= 3/2

lo g_{x} (512) = \frac{3}{2}

x = 64

Solution steps

lo g_{x} (512) = \frac{3}{2}

Apply log rules

\frac{1}{lo g _{512} ( x )} = \frac{3}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{512} (x) \cdot 3

Simplify

2 = lo g_{512} (x) \cdot 3

Switch sides

lo g_{512} (x) \cdot 3 = 2

Divide both sides by

3

lo g_{512} (x) = \frac{2}{3}

Apply log rules

x = 64

Verify Solutions:

x = 64

True

The solution is

x = 64

y, lo g_{x} (y) = 2

ln (4) - ln (3) = 2 ln (x) - ln (x + 1)

lo g_{2 - x} (2 x^{2} - 5 x + 2) = 2

4 = - lo g_{10} (x)

lo g_{8} (4 x + 4) = 2

What is the answer to log_{x}(512)= 3/2 ?
The answer to log_{x}(512)= 3/2 is x=64
Solve for x: log_{x}(512)= 3/2
The solution is x=64